Help needed for boundary condition treatment for cavity flow. The flow solver is for 2D compressible NS equations, while the Mach number is set to about 0.1. And do you think the results from this setting can be comparable with that from an imcompressible flow solution(same Re number)?

(1). It is a rather vague question. (2). Even within the framework of the incompressible solutions, the solution obtained depends on the formulation and the algorithm used, not to mention the effect of the Reynolds number. (3). Different algorithms will produce different solutions, as a strong function of the Reynolds number. (4). If the compressible flow formulation is transient, there is no guarantee that a steady state solution will be found. (5). Mach number=0.1 is within the incompressible flow regime. It simply says that the effect of density on the solution is small. (that is the compressibility effect)

The thing is that I just found a case of incompressible cavity flow, the Re number is 400. (Shuen(1993, JCP) and Soh(1988, JCP)). I want to use it as a validation case for my code. In both of the previous simulation, the flowfield was steady after Time = 36.

In my code, the velocity looks fine. However the pressure is decreasing along time marching steadily. For a incompressible flow, that is fine if the pressure gradient is right. However for a compressible flow code, this is a problem. I think the pressure should be prescribed at some point. However due to all boundaries are walls, the pressure can not be precribed.

(1). At Re=400, the flow should be laminar and steady state. And this condition has been studied for a long time. (2). For the compressible flow approach, since it is a sealed system, the cavity must be initially pressurized. That is the pressure field specified , consistent with the initial temperature and the density. This is easy for stationary system, with a constant density, temperature and pressure. Then you can start the motion of the lid and solve the transient equation. (3). If the wall is adiabatic (insulated), the work done on the system will heat up the cavity through the moving lid. As a result, the temperature and the pressure will increase. It is a transient problem. (4). Or you can use the constant temperature wall condition. In this way, I think, it is possible to have a steady state solution. Anyway, the closed system is self-contained, the total mass is always constant.